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x /.

There aie two practical applications of this problem to which
reference may be made. The first is where a locomotive boiler-
barrel is sometimes flattened to save width, and the flat portion
becomes such a beam as we have discussed, the supports being
then represented by stay "bolts. The other example is that of a
paddle-wheel float, when supported by the float arms at two
places only.

An extension of the problem is shewn in Fig, 754. There
are two supports, A and E, but the former is a hinge. Using
similar letters,

oc = by        b ='4 1 4/,        /=L-#=L b
^,           and    

A similar case, but with concentrated load at c, is that of the
wall crane, Fig. 754.

P. 445. Continuous Beams.  The following is a simple
method of finding the reactions on the supports in the case of
a beam over two spans.

Suppose the mid-support be removed, a deflection will be
caused by the uniform load, 2 Wlt

48 El

(See pp. 451 and 849.)

Now the upward pressure that would neutralise this deflection
would have the same value as a concentrated load capable of
causing it. Let this load = R: then the deflection caused by R,

A<> =.........o -r->T     and equating the two values,

40 E* *



48 El ~   4&EI

whence E. =